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Theorem nfim1 1811
 Description: A closed form of nfim 1813. (Contributed by NM, 5-Aug-1993.) (Revised by Mario Carneiro, 24-Sep-2016.) (Proof shortened by Wolf Lammen, 2-Jan-2018.)
Hypotheses
Ref Expression
nfim1.1 xφ
nfim1.2 (φ → Ⅎxψ)
Assertion
Ref Expression
nfim1 x(φψ)

Proof of Theorem nfim1
StepHypRef Expression
1 nfim1.1 . . . 4 xφ
21nfri 1762 . . 3 (φxφ)
3 nfim1.2 . . . 4 (φ → Ⅎxψ)
43nfrd 1763 . . 3 (φ → (ψxψ))
52, 4hbim1 1810 . 2 ((φψ) → x(φψ))
65nfi 1551 1 x(φψ)
 Colors of variables: wff setvar class Syntax hints:   → wi 4  Ⅎwnf 1544 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-11 1746 This theorem depends on definitions:  df-bi 177  df-ex 1542  df-nf 1545 This theorem is referenced by:  nfim  1813  sbco2d  2087
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